Dissociation Equilibrium and Charge Carrier Formation in AgIâAgPO3

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Dissociation Equilibrium and Charge Carrier Formation in AgI-AgPO Glasses Caio Barca Bragatto, Ana Candida Martins Rodrigues, and Jean-Louis Souquet J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 02 Jun 2017 Downloaded from http://pubs.acs.org on June 6, 2017

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The Journal of Physical Chemistry

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Dissociation Equilibrium and Charge Carrier Formation in AgI-AgPO3 Glasses Caio Barca Bragatto, Ana Candida Martins Rodrigues*, Laboratório de Materiais Vítreos (LaMaV), Universidade Federal de São Carlos (UFSCar), São Carlos, SP, Brazil

Jean-Louis Souquet Laboratoire d’Electrochimie et de Physicochimie des Matériaux et des Interfaces (LEPMI) GrenobleINP, Saint Martin D’Hères 38401, France *[email protected]

Abstract: The x AgI (1-x) AgPO3 glass system exhibits a wide and well known range of variation in silver ion conductivity with the AgI molar ratio, x, while the total concentration of Ag+ ions does not change significantly. We propose an interpretation to explain this effect, based on the fact that only a fraction of Ag+ cations are effective charge carriers, and that their concentration is determined by a dissociation equilibrium of AgI in the AgPO3 glass. In this case, the ionic conductivity stems from the thermodynamic activity of silver iodide, aAgI, dissolved in the AgPO3 glass. To verify this relationship experimentally, aAgI is determined from electromotive force (EMF) measurements of solid state cells in the temperature range of 25 to 90°C. Our results reveal a linear dependence of silver ion conductivity on aAgI over three orders of magnitude. The substantial variations in aAgI observed with the increase in the AgI molar ratio x are justified assuming a regular solution model for the AgI-AgPO3 mixture.

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1. Introduction Remarkable ionic conductivity in glass was first observed in 1973 by Kunze1 in AgI-Ag2MoO4 glass. Following this finding, systematic studies of AgI dissolved in different glassy matrices have revealed that conductivity increases significantly as a function of AgI content. The first glassy matrices that were studied were Ag2MoO4 2, AgPO3 3, and AgBO2 4, later followed by more complex glassy matrices such as sulfoxides5 and sulfides5,6. Measurements of transport numbers in AgI-AgPO3 glasses taken by Malugani3 confirmed that ionic conductivity in these silver glasses is due solely to Ag+ cations. The increase in ionic conductivity in response to augmented AgI content depends on the glassy matrix, and at room temperature, may correspond to an enhancement of 3 to 5 orders of magnitude, reaching up to a maximum value of close to 10-2 S cm-1 at room temperature in all glass systems.7

Numerous structural approaches, albeit few thermodynamic ones, have been developed to explain this enhancement in ionic transport as a function of AgI content in various AgI containing glasses.

Among the structural approaches, there is a consensus that AgI does not significantly modify the network-forming structure and only intercalates between phosphate chains or rings8-10. The structural models that have been proposed differ from each other only with respect to the degree of local organization of AgI molecules. The “cluster model” assumes the existence of AgI microdomains containing conductive Ag+ ions9,11. These microdomains were initially interpreted as being composed of a highly conductive crystalline α-AgI phase, usually stable above 140°C, which would be stabilized at lower temperatures by the surrounding glassy matrix.9,12,13 As the AgI content increases in the glass composition, the clusters presumably percolate, leading to an overall increase in conductivity.14 Other structural approaches have been proposed, also based on a heterogeneous structure of glass, such as the “diffusion path model,” in which mobile silver cations are coordinated mainly by iodide15-17, or the “cluster tissue model,” with a high local concentration of iodine that ensures high silver cation mobility. In these models, as


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proposed by Ingram18, a highly conductive interconnected AgI-rich “tissue” would surround the lower conducting phase of the host network. Swenson et al.19, who used the reverse Monte Carlo method to model neutron and X-ray diffraction and EXAFS data, found a homogeneous distribution of AgI between the phosphate chains in AgPO3-AgI glasses. A random distribution of anions was confirmed by a NMR study of AgI-Ag3PO4 glasses.20 Considering those findings, some authors have suggested that AgI molecules expand the glass structure, facilitating the displacement of Ag+ cations19,21. However, these structural interpretations are qualitative and do not offer a quantitative explanation of the quasi-exponential increase in conductivity with AgI content. From another point of view, a thermodynamic approach was developed in accordance with an homogenous glass structure, in which AgI is considered a solute dissolved in a solvent glass and partly dissociated to generate ionic charge carriers.7,22,23 The enhanced conductivity, in this case, would be correlated to the free energy of AgI or, in other words, to the increase in AgI thermodynamic activity. Reggiani et al. experimentally verified this thermodynamic model, derived from the so-called “weak electrolyte model”24, by calculating the AgI activity, aAgI, from dissolution calorimetry measurements and proposed the hypothesis of a regular solution model for AgI-AgPO3 glasses.22 The relationship of σ = (aAgI)0.6 they found was justified by a dissociation equilibrium of AgI in the glass, which would generate the effective charge carriers. A slightly different relationship, σ = (aAgI)≈1, for glassforming systems such as AgI-Ag3PO4, AgI-Ag4P2O7, AgI-Ag2MoO4 and AgI-Ag2Cr2O7, was proposed by Grande25, based on an analysis of the phase diagrams corresponding to these glass-forming melts using the Clausius-Clapeyron relation. Both techniques, calorimetry and phase diagram analysis, only allow for indirect assessments of the thermodynamic activity of AgI.

In this work, the thermodynamic activity of AgI in glasses of the x AgI (1-x) AgPO3 (0.1 ≤ x ≤ 0.5) system was measured directly using appropriate electrochemical cells. Hence, the evolution of the thermodynamic activity of AgI will



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be related to that of ionic conductivity resulting from the increase in the molar ratio of AgI. This system was chosen because of the high sensitivity of ionic conductivity to composition, as shown in Figure 1. In addition, glasses in the AgI-AgPO3 system have been widely investigated and characterized by different complementary techniques, and information on numerous physical characteristics is available, such as density, glass transition and viscosity.26-28 AgI-AgPO3 glasses are stable and easily synthesized, with a glass forming domain covering a large compositional range and an AgI molar ratio, x, of up to 0.5. Their glass transition temperatures (Tg) lie in the range of 140 to 180 °C.

-2

-1

-3

log (σ), σ in S cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-4

x AgI (1-x) (0.5 Ag2O 0.5 P2O5)

-5

x AgI (1-x) (0.5 Ag2O 0.5 B2O3) x AgI (1-x) (0.5 Ag2S 0.5 As2O3) -6

x AgI (1-x) (0.5 Ag2S 0.5 P2S5) x AgI (1-x) (0.67 Ag2S 0.33 P2S5) x AgI (1-x) (0.5 Ag2S 0.5 GeS2)

-7 0.0

0.1

0.2

x

0.3

0.4

0.5

Figure 1 – Logarithm of ionic conductivity at 25 oC versus molar ratio of silver iodide (x) in different glass systems. Adapted from [7].

2. Materials and Methods


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The “solvent glass” AgPO3 was prepared by melting and quenching an equimolar mixture of AgNO3 and NH4H2PO4 powders with purity over 99.5% from Sigma Aldrich, USA. After 1h of melting at 500°C in a borosilicate crucible (Pyrex ®), liquid drops were splat quenched at room temperature between two stainless steel plates. Glass samples synthesized at this moderate temperature were uncolored and transparent, indicating that no Ag2O decomposition occurred during melting. AgPO3 glass, finely crushed, was then mixed with appropriate amounts of AgI (Sigma Aldrich 99.5% purity, USA), melted again at 500°C in a Pyrex® crucible, and splat quenched. Glass samples, with different compositions in the x AgI (1-x) AgPO3 system were produced by this procedure. Their amorphous structure was confirmed by X-ray diffraction (XRD) for x=0.0, 0.1, 0.2, 0.3, 0.4 and 0.5. The AgPO3 glass with x=0.7 was saturated in AgI and the excess silver iodide, precipitated in the glass as crystalline β-AgI, was identified by XRD (pattern not shown here).

The chemical composition of the glass samples was examined by X-ray fluorescence spectroscopy (XRF), which revealed that they corresponded to their nominal composition, with the I/Ag and P/Ag molar ratios showing a discrepancy of less than 5% from the nominal one. Densities were determined by gas (Helium) pycnometry and glass transition temperatures by Differential Scanning Calorimetry (DSC, Netzsch 404) at a heating rate of 10 K min-1.

For electrical conductivity measurements, disc shaped samples about 8mm in diameter and 1 mm in thickness, were obtained by the previously described splatcooling of melt droplets. Gold electrodes were sputtered (Quorum QR150 RES Sputter) onto the two circular sides of the samples. The resistance of the samples was determined by impedance spectroscopy in a frequency range of 10MHz to 5Hz, using a Solartron 1260 Impedance/Gain-Phase Analyzer coupled to a Solartron 1296 dielectric interface system. The samples were placed in a two-point sample holder, which was inserted into a Janis (CSS-400 H/204) cryostat for measurements below room temperature. Impedance data were plotted in the complex plane plot. The resistance (R) of the sample was determined from the intersection of the impedance semicircle and the real axis, at low frequencies. Ionic conductivity (σ) was then



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calculated using the relation σ

=

,

where l and S correspond, respectively, to

the sample´s thickness and area.

To determine the thermodynamic activity of AgI, two sets of solid-state cells corresponding to two different electrochemical chains were prepared:

(-) Ag | β-AgI | C, I2 (+)

(1)

(-) Ag | x AgI (1-x) AgPO3 glass | C, I2 (+)

(2)

These cells associate an Ag+ conductive solid electrolyte (β-AgI or x AgI-(1-x) AgPO3 glass) with a silver electrode and a (graphite C, I2) iodine electrode. The EMF delivered by cells 1 and 2 is hereinafter referred to as EMF1 and EMF2, respectively. EMF1 can be compared to results previously obtained by Bradley and Greene29 on the same cell.

The silver Iodide was supplied by Alfa Aesar (USA) (99.9%) and the silver powder, graphite and iodine, with 99.98 and 99.5% purity, respectively, came from Synth (Brazil).

The solid-state cells were prepared by successive compactions of: i) silver powder, ii) a mixture of silver and solid electrolyte powders, iii) the ground solid electrolyte, iv) a mixture (1/1) of solid electrolyte and graphite-iodine (C, I2) powders, and v) a graphite-iodine mixture (C, I2) in a volume of 1/1. The two intermediate layers of the mixtures of solid electrolyte and electrode materials (1/1 volume) allowed for optimization of the interfacial contacts between electrodes and solid electrolyte. Finally, the electrochemical cells were composed of five successively compacted layers, each about 1mm thick and 8mm in diameter. Pellets were compacted at 5 GPa cm-2 in a stainless metallic mold. The solid-state cells were then placed in a Büchi B-585 glass oven and their voltage (EMF) was measured using an


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Agilent 34461A multimeter with a high input impedance of 10 GΩ and recorded in the temperature range of 25-90°C.

3. Results

Figure 2 represents the evolution of density and the glass transition temperatures Tg for x AgI (1-x) AgPO3 glasses as a function of composition. Both properties present a linear variation when x varies from x = 0 to x = 0.5.

5.4 160 5.2 140

-3

5.0 o

Tg, in C

Density, in g cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

120

4.8

4.6 100 4.4 80 0.0

0.1

0.3

0.2

0.4

0.5

x

5.4by He pycnometry (left) and DSC (10K min-1) glass Figure 2 – Density measured

transition temperature (right) x AgI (1-x) AgPO3 glasses as a function of the molar ratio (x). Both properties present a linear behavior with x. The decrease in glass transition temperature with x can be attributed to the “plasticizer effect” of AgI, which is presumably inserted between the macromolecular



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phosphate chains, decreasing the numerous ionic interactions that occur between neighboring phosphate chains.30 The linear increase in density can be understood by -

assuming that the PO4 tetrahedrons in the anionic network are progressively -

substituted by an anion, both of a similar size (2.38 Å for a PO4 tetrahedron, 2.14 Å for an anion)31, but with a larger mass for the iodide anion, (M(I)=127 g/mol and M(PO3)=79

g/mol).

Consequently,

the

cationic

silver

sublattice

remains

approximately unchanged by this substitution, as evidenced in Table 1, where the concentration of silver cations, , calculated from density data, increases only slightly with x.

Table 1. Density obtained by gas (Helium) pycnometry and concentration of silver ions calculated from density.

x (molar ratio) in x AgI (1-x) AgPO3

Density, in g cm-3

, in atoms cm-3

0.0

4.45 ± 0.05

1.43 1022

0.1

4.66± 0.05

1.46 1022

0.2

4.80± 0.05

1.47 1022

0.3

5.05 ± 0.05

1.51 1022

0.4

5.18± 0.05

1.51 1022

0.5

5.39± 0.05

1.54 1022

Figure 3 represents, in Arrhenius coordinates, ionic conductivities of x AgI (1x) AgPO3 glasses expressed as the σ T product in the temperature range of -100°C to 100°C.


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o

T, in C 100

50

0

-50

-100

AgPO3 0

x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5

-1

log (σ.T), σ.T in K S cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-2

-4

-6

-8 3

4

5

-1

6

-1

T , in 1000 K

Figure 3 – Arrhenius representation of the ionic conductivity of the x AgI (1-x) AgPO3 glasses, measured by impedance spectroscopy.

The ionic conductivity as a function of temperature confirmed the relation:

=

(3)

where EA is the activation energy for ionic transport and A is a temperature independent pre-exponential term. Table 2 lists the experimental values of these two parameters for the six investigated glass compositions.



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Table 2 – Ionic conductivity at room temperature, activation energy for ionic conduction, and pre-exponential term Α of Arrhenius expression (1) for x AgI (1-x) AgPO3 glasses. These results were obtained by the linear regression of experimental data presented in Figure 3. The indicated errors are the mathematical ones, rounded up to one (constant A), or two (Activation energy) decimal places.


Conductivity at 25 oC (S cm-1)

Activation energy (eV)

Constant A 104 (K S cm-1)

0

1.4 10-7

0.55 ± 0.01

9.1 ± 0.2

0.1

1.9 10-6

0.47 ± 0.01

6.4 ± 0.2

0.2

-5

0.41 ± 0.01

4.5 ± 0.2

0.3

-5

7.4 10

0.38 ± 0.01

5.8 ± 0.2

0.4

4.9 10-4

0.31 ± 0.01

3.0 ± 0.2

0.5

-3

0.25 ± 0.01

1.8 ± 0.2

1.6 10

3.4 10

The pre-exponential term, A, presents values between 104 to 105 K S cm-1, in agreement with a cationic jump model32 between two silver cationic sites. According to this model:

=

2

2 λ ν0 6#$

(4)

)

where is the concentration of silver cations, % = &1⁄ is the mean distance between two silver ions, ν0 is the jump attempt frequency, and

and #*

are the

electronic charge and Boltzmann constant, respectively. Assuming reasonable values of ν0 = 1013 Hz, n=1022 Ag+ cations cm-3 allows for a numerical estimation of A = 5.0 104 K S cm-1, which is in agreement with the experimental values reported in Table 2. Note that, compared to the four order of magnitude variation of ionic conductivity, the pre-exponential term A seems constant with the increase of AgI content (x), in the glass series x AgI (1-x) AgPO3.


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Electromotive forces (EMF) delivered by the previously described solid-state cells are measured as a function of temperature between room temperature and 90°C, in increments of about 10°C. Each temperature increment requires a stabilization time of about 3 hours. Figure 4 shows an example of the variation in EMF during successive temperature increments in the cell (-) Ag | β-AgI | C, I2 (+).

Figure 4 – Electromotive force and temperature variations as a function of time of the electrochemical cell (-) Ag | β-AgI | C, I2 (+). Each temperature plateau lasts for approximately 3 hours.

Figure 5 reports measured EMF data delivered by cells 1 and 2. EMF values were considered at equilibrium when their variations were lower than ± 5 mV during 2 hours.



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Figure 5 – Electromotive force of the electrochemical cells (-) Ag | β-AgI | C, I2 (+) (EMF1), and (-) Ag | x AgI (1-x) AgPO3 glass | C, I2 (+) (EMF2), with x varying from 0.1 to 0.5.

4. Discussion

4.1 The (-) Ag | β-AgI | C, I2 (+) cell

The virtual electrochemical reaction in this cell is the formation of β-AgI according to the global reaction: 7

∆3456

+,-. / ½ 1,-. 8999: ;+ ,-.

implying the two electrode reactions. At the anode


(5)

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+,-. → += /

(6)

½ 1 ,-. / →

(7)

and at the cathode:

?

The corresponding free energy for the formation of β-AgI, ∆>;+ , is the difference in free energy of the final product and the reactants, C

∆>A B = >A B − > ,E. − ½>BF ,-.

(8)

The measured EMF1 can thus be written as:

EMF1 = −

?

∆>;+

(9)

G

The variations in EMF1 with temperature allow calculating the change in entropy according to

HIJK1 H L

=

?

∆M;+ K

, where

NOGP N

is the EMF variation with Q

temperature at constant pressure and F is the Faraday constant Thus, from the values of EMF1 as a function of temperature, it is possible to calculate the changes in C

C

enthalpy and entropy, ∆RA B and ∆MA B , associated with the virtual reaction 5. Our results, which are presented in Table 3, are in agreement with the entropy and enthalpy of formation of AgI described in the thermodynamic tables of Kubaschewski et al. 33, and with a similar cell studied by Bradley and Greene.29



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C

C

Table 3 – Entropy, ∆MA B , and enthalpy, ∆RA B , of β-AgI formation in the standard state obtained from the literature and in this work.

Kubaschewski et al. [33]

Bradley & Greene [29]

This work

13

14.5

19.9

-61.7

-66.5

-60.1

C

∆MA B (J K mol-1) C

∆RA B (kJ mol-1)

4.2 The (-) Ag | x AgI (1-x) AgPO3 glass | C, I2 (+) cells

The expected virtual electrochemical reaction, in this case, would be the formation of AgI in the glass according to the global reaction: 7

∆356,5VWEE.

+,-. / ½ 1,-. 89999999: + XY--

(10)

with a corresponding EMF2:

IJK1 = −

7

∆3456 =356,5VWEE. G

= −

7

∆3456 =Z [ Y56 G

(11)

where > B,XY--. and aAgI are, respectively, the partial free energy and the thermodynamic activity of AgI dissolved in the glass, referred to pure β-AgI. Since the free energy of dissolved AgI in the glass is lower than that of pure β-AgI, the

\ ln ^ B term is negative which means that aAgI, referred to pure AgI, is lower than unity, and the expected measured EMF2 should be higher than EMF1. However, experimentally, the opposite behavior is observed, that is, a lower value for EMF2 increasing at constant temperature with the amount of AgI dissolved in the glass, until EMF1 is reached, when the cell electrolyte is pure β-AgI (Figure 5).


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This behavior can be explained based on the assumption that the cell reaction leads to a β-AgI layer at the glass / (C, I2) interface, since AgI cannot dissolve due to an iodine transport number close to zero in the glass. The electrochemical chain may thus be written as:

(-) Ag | x AgI (1-x) AgPO3 | β-AgI | C, I2 (+)

(12)

The introduction of a β-AgI layer between the glass electrolyte and the (C, I2) electrode leads to the development of an AgI concentration cell between β-AgI and the glass. The virtual electrochemical reaction corresponding to this concentration cell is a transfer of AgI from the β-AgI layer to the glass. The transfer of Ag+ silver cations would occur from β-AgI to the glass, since both are silver conductive. The electroneutrality would be respected by the introduction of an iodine anion at the silver electrode, according to the reaction ½ I2 + ⇄ , for which the metallic silver acts as the electron source and I2 is provided by the surrounding iodine vapor. Finally, the EMF3 of this concentration cell can be written as:

IJK` = −

a56,5VWEE. 3456 G

= −

356,5VWEE. G

= −

Z [ Y56

(13)

G

Because EMF3 is in opposite polarity to EMF1, the measured EMF2 is rewritten as:

IJK1 = IJK − IJK` = IJK /

ZXb Y56

(14)

G

Thus, for each glass composition,

log ^ B = K

OGF OGP 1.` Z


(15)


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Table 4 lists the calculated values at 25°C for log aAgI as a function of the AgI molar ratio x, using expression 15 and EMF data reported in Figure 5. In this table, the values of AgI activities are compared with another set of data deduced from dissolution calorimetry measurements of glasses with the same composition taken by Reggiani.22 The slight difference between the two data sets may be attributed to the ideal value of the entropic term estimated by the author, in addition to the enthalpic one determined by calorimetry.

Table 4 – log aAgI at 25°C calculated from expression (15) for x AgI (1-x) AgPO3 glasses obtained by electromotive force measurements (this work – Figure 5), and by dissolution calorimetry.22

log aAgI


Reggiani et al. [22]

This work

0.1

-3.9

-3.5

0.2

-3.7

-2.4

0.3

-2.6

-1.6

0.4

-0.2

-1.0

0.5

0.5

-0.2

4.3 Ionic conductivity and AgI thermodynamic activity

From the EMF measurements shown in Figure 5, we calculated aAgI, referred to β-AgI, for all the studied glass compositions at five selected temperatures, using expression 15. These calculated values are plotted as a function of the conductivity corresponding to the same glass composition in a log/log scale graph, Figure 6. The variation in log conductivity as a function of log aAgI accurately defines a straight line with a slope of 1, suggesting the following simple proportionality relationship at all the temperatures:


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fg+ ∝ fg+^ B gi ∝ ^ B

-1

-2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-3

(16)

Temperature: o 25 C o 45 C o 55 C o 65 C o 75 C Slope = 1

-4

-5

-3

-2

-1

0

log aAgI

Figure 6 – Dependence of log σ on log aAgI at different temperatures, and for different glass compositions of the glass system x AgI (1-x) AgPO3. The full line serves as a visual guide.

4.4 Suggested mechanism for Ionic transport In the investigated glass system, ionic transport is due exclusively to Ag+ cations and depends on the product of the effective concentration of charge carriers +

n+ and their mobility µ

.

σ = e n+ µ+

(18)



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18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Ag+ mobility values at room temperature reported in a previous article23 were calculated from conductivity data below and above the glass transition for the glasses of the x AgI (1-x) AgPO3 system.34 The calculated values are in agreement with mobility data previously determined by Hall effect measurements.35 Mobility appears to be independent of the AgI content, x, with a mean value of 5 10-4 cm2 V−1 s−1 at room temperature. Thus, using equation 18 and experimental conductivity data at the same temperature, mobility values allow one to calculate the concentration of effective charge carriers, n+. Since the total concentration (n) of Ag+ ions is estimated from density (Table 1), the n+/n ratio may then be assessed. At room temperature, this n+/n ratio increases from 10-8 to 10-3, when x varies from 0.0 to 0.5.23 These low values of n+/n ratio mean that not all the silver cations participate in the conduction process at the same time, but only few of them that received the minimal free energy

∆Gf from the available thermal energy to become a charge carrier. This low concentration of effective charge carriers can be compared to the concentration of charged point defects (interstitial pairs) in silver ion crystals, or to the concentration of hydronium cation, H3O+, in water.36 Based on this comparison, Figure 7 represents a possible mechanism for charge carrier formation by transfer of a silver cation from an AgI molecule to a neighboring one (dashed line), forming an Ag2I+ cation. After formation of the charge carrier, Ag+ may then migrate in the direction imposed by an external electric field (solid line) from one AgI molecule to another.


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Figure 7 – Formation of the cationic pair described by the equilibrium dissociation 2AgI ⇄ Ag2I+ + I- and migration of the charge carrier. Now, considering the equilibrium between the different species produced in this self-ionization process: n klmEE

2+ ⇌ +1 / / -

(19)

the dissociation constant KTdiss can be expressed as a function of the energy required for the formation of this charge carrier, ∆Gf, and the thermodynamic activity of the components

opq-= -

r37

=

Y5 6+ . Y6− F F Y56

=

s t F B + us− tB − u F Y56


(20)


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Assuming constant values for the activity coefficients γ+/- of ionic species at low concentrations and the electroneutrality condition, [Ag2I+] = [I-], the above equilibrium is reduced to:

o′pq-- =

t F B / uwB - x F Y56

=

t F B / uF F Y56

(21)

Finally, the charge carrier concentration, [Ag2I+], is simply proportional to the AgI thermodynamic activity, aAgI, as found experimentally and expressed by equation (16). / 1

2 or t+1 / u ∝ ^+ w+2 x ∝ ^+

(22)

It is worth mentioning that, according to the jump model, the entity that moves is silver ions Ag+ from one I- anion to another. However, the concentration of effective charge carriers in a given instant will be the same as the ionic triplets, or interstitial defects t+1 / u. This also means that not all the silver ions will move simultaneously at a given time, but after a long time, compared to a cationic transfer from one AgI molecule to another, all the silver ions will have moved. This reasoning was also applied in the case of alkali silicate37, and a time interval of 10-2 s has been estimated to allow all cations to move.

4.5 AgI thermodynamic activity estimated by means of a regular solution model

After correlating the significant variation in conductivity to the variations in AgI thermodynamic activity, the clear and important dependence of this activity on the AgI molar ratio, x, in the x AgI (1-x) AgPO3 glass system, remains to be justified.

As a first approximation, we will choose the regular solution model, which is usually considered representative of most molten salt mixtures with a common cation


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and two different associated anions.38 In the present case, the composition is defined by the molar ratio x. The regular solution model is based on the hypothesis of a symmetric mixing enthalpy yRzq{ = −|,1 − ., where α is an interaction parameter related to the reorganization of ionic bonds after mixing and of an ideal mixing entropy − #* tf ,. / ,1 − .f ,1 − .u resulting from the mixing of two different anions, in this case, and PO3 . -

The total mixing free energy is then expressed by: y>zq{ = −| ,1 − . / \tf , . / ,1 − .f ,1 − .u

(23)

The Gibbs-Duhem equation allows one to access the partial free energy of AgI: > B = y>zq{ / ,1 / .

Nr3}m~ N{

= \f , . − |,1 − .1 = \ f ^ B (24)

in which the thermodynamic activity of AgI as a function of x is expressed as:

fg+ ^ B = fg+ −

, {.F 1.`Z

(25)

AgI activity calculated from EMF measurements and reported in Table 4 can subsequently be fitted to this expression, allowing for the graphical determination of the α parameter. The corresponding best fit leads to a value of α = 14.6 kJ mol-1 and is represented in Figure 8.



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22

Regular Solution model with α = 14.6 kJ mol-1

0

-1

log aAgI

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-2

-3

-4 0.1

0.2

0.3

0.4

0.5

x Figure 8 – log aAgI as a function of x, at 25oC, for the investigated glasses. The line represents the best fit for equation 18, with α = 14.6 kJ mol-1.

This value is in a good agreement with the usual mixing enthalpy for molten salt mixtures, representing the change in ionic interactions due to the mixing of two different anions.38,39 It is also close to the experimental value determined by dissolution calorimetry by Reggiani et all22 for AgI-AgPO3 glasses In fact, these authors measured a maximum value of yRzq{ = 4.14 kJ mol-1 for x=0.35, corresponding to α = 18.2 kJ mol-1. Also in Figure 8, the discrepancy between the calculated and experimental variations of log aAgI with composition may be due to the choice of a symmetric mixing enthalpy with x, yRzq{ = −|,1 − . , to calculate activities values. In contrast, experimental calorimetric data of Reggiani indicate a slight asymmetric variation of ∆Hmix with a minimum value for x=0.35, indicating a deviation from the symmetric mixing enthalpy chosen here as a first approximation.


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5. Conclusions

Based on a classical approach for electrolytic solutions, this paper seeks to explain that a simple dissociation equilibrium may justify the large variations in Ag+ conductivity observed in the x AgI (1-x)AgPO3 glass system as a function of the AgI molar ratio, x. Linking conductivity data to the measured thermodynamic activity of AgI at the same temperature, the following proportionality relationship is verified:

∝ ^ B This proportionality relation is interpreted by assuming the dissociation equilibrium: n klmEE

2+ ⇌ +1 / / in which the concentration of effective charge carriers is identified for the concentration of +1 / cations. The dissociation process leads to a huge variation in the effective concentration of charge carriers, which is proportional to a huge variation in the thermodynamic activity of AgI in the glass: t+1 = u ∝ ^+ Finally, isothermal variations in ionic conductivity as a function of x depend mainly on charge carrier concentration and do not imply wide variations in their mobility.

The important variations in AgI thermodynamic activity as a function of composition in the AgI-AgPO3 glasses with a mixing enthalpy of the same order of magnitude as that of ordinary molten salt mixtures are interpreted by means of a regular solution model.



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Acknowledgments The authors gratefully acknowledge the Brazilian research funding agencies CAPES (Federal Agency for the Support and Improvement of Higher Education) (PVE – A005-2013. Process No. 23038.007714/2013-40) and the São Paulo State Research Foundation – FAPESP (process number 2011/10564-3 and CEPID process N. 2013/07793-6). C. B. Bragatto is also indebted to the Postgraduate Program in Materials Science and Engineering – PPG-CEM, of UFSCar/DEMa for its financial support. J.-L. Souquet thanks LaMaV for its hospitality while participating in this research work.

References

1- Kunze, D. In Fast Ion Transport in Solids; Van Gool W., Ed.; North-Holland: Germany, 1973.

2- Minami, T.; Nambu, H.; Tanaka, M. Comparison of Ionic Conductivity Between Glassy and Crystalline Solid Electrolytes in the System AgI-Ag2O-MoO3. J. Am. Ceram. Soc. 1977, 60, 467-469. 3- Malugani, J-P.; Wasniewski, A.; Doreau, M.; Robert, G. Conductivite Electrique et Spectres de Diffusion Raman des Verres Mixtes AgPO3− MI2 Avec M = Cd, Hg, Pb. Correlation entre Conductivité et Structure. Mater. Res. Bull. 1978, 13, 427– 433. 4- Magistris, A.; Chiodelli, G.; Schiraldi, A. Formation of High Conductivity Glasses in the System AgI-Ag2O-B2O3. Electrochimica Acta 1979, 24, 203-208. 5- Robert, G.; Malugani, J-P.; Saida, A. Fast Ionic Silver and Lithium Conduction in Glasses. Solid State Ionics 1981, 3-4, 311-315. 6- Robinel, E.; Carette, B.; Ribes, M. Silver Sulfide Based Glasses (I). Glass Forming Regions, Structure and Ionic Conduction of Glasses in GeS2-Ag2S And GeS2Ag2S-AgI Systems. J. Non-Crystalline Solids 1983, 5, 49-58.


Page 25 of 29


25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

7- Kone, A.; Souquet, J-L. Thermodynamic Approach to Ionic Conductivity Enhancement by Dissolving Halide Salts in Inorganic Glasses. Solid State Ionics 1986, 18-19, 454-460. 8- Malugani, J-P.; Mercier, R. Vibrational Properties of and Short Range Order in Superionic Glasses AgPO3−AgX (X = I, Br, Cl). Solid State Ionics 1984, 13, 293299. 9- Tachez, M.; Mercier, R.; Malugani, J-P.; Chieux, P. Structure Determination of AgPO3 and (AgPO3)0.5(AgI)0.5 Glasses by Neutron Diffraction and Small Angle Neutron Scattering. Solid State Ionics 1987, 25, 263-270. 10- Kamitsos, E. I.; Kapoutsis, J. A.; Chryssikos, G. D.; Hutchinson, J. M.; Pappin, A. J.; Ingram, M.D.; Duffy, J. A. Infrared Study of AgI Containing Superionic Glasses. Phys. Chem. Glasses, 1995, 36, 141-149. 11- Schiraldi, A. AgI-Ag Oxysalt High Conductivity Glasses: a Tentative Approach to their Structure. Electrochem Acta 1978, 23, 1039-1043. 12- Tatsumisago, M.; Shinkuma, Y.; Saito, T.; Minami, T. Formation of Frozen α-AgI in Superionic Glass Matrices at Ambient Temperature by Rapid Quenching. Solid State Ionics 1992, 50, 273-279. 13- Minami, T. New Borate Glasses for Ionics. Phys. Chem. Glasses 2012, 53, 17– 26. 14- Mangion, M. B. M.; Johari, G. P. The Dielectric Behavior and Conduction of AgIAgPO3 Glass of Various Compositions Phys. Chem. Glasses 1988, 29, 225–234. 15- Minami, T., Fast Ion Conducting Glasses. J. Non-Crystalline Solids 1985, 73, 273-284. 16- Nakayama, M.; Hanaya, M.; Hatate, A.; Oguni, M. Glass Structure and Energetic Environment around Conducting Ag+ Ion in AgI-Based Fast Ion Conducting Glasses (AgI)X (AgPO3)1−X Studied by Calorimetry and Dielectric Measurement. J. Non-Crystalline Solids 1994, 172-174, 1252-1261.



Page 26 of 29

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17- Tomasi, C.; Mustarelli, P.; Magistris, A.; Garcia M. P. I. Electric, Thermodynamic and NMR Evidence of Anomalies in (X) AgI (1−X) AgPO3 Glasses. J. NonCrystalline Solids 2001, 293- 295, 785-791. 18- Ingram, M.D. Ionic Conductivity in Glass. Phys. Chem. Glasses 1987, 28, 215234. 19- Swenson, J.; Mcgreevy, R. L.; Börjesson, L.; Wicks, J.D. Relations Between Structure and Conductivity in Fast Ion Conducting Glasses. Solid State Ionics 1998, 105, 55–65. 20- Ren, J., Eckert, H. Anion Distribution in Superionic Ag3PO4–AgI Glasses Revealed by Dipolar Solid-State NMR. J. Phys. Chem. C 2013, 117, 24746−24751. 21- Sidebottom, D. L. Influence of Cation Constriction on the AC Conductivity Dispersion in Metaphosphate Glasses. Phys. Rev. B, 2000, 61, 14507-14516. 22- Reggiani, J-C.; Malugani, J-P.; Bernard, J. Étude des Systèmes Vitreux AgPO3AgX (X= I, Br, Cl) Par Calorimétrie De Dissolution. Corrélation entre l’Activité Thermodynamique de AgX et la Conductivité Ionique du Verre. Journal De Chimie Physique 1978, 75, 245-249. 23- Rodrigues, A. C. M.; Nascimento, M. L. F.; Bragatto, C. B., Souquet, J-L. Charge Carrier Mobility and Concentration as a Function of Composition in AgPO3-AgI Glasses. J. Chem. Phys. 2011, 135, 234504-7. 24- Ravaine, D.; Souquet, J.-L. A Thermodynamic Approach to Ionic Conductivity in Oxide Glasses. Part 1. Correlation of the Ionic Conductivity with the Chemical Potential of Alkali Oxide in Oxide Glasses. Phys. Chem. Glasses. 1977, 18, 27– 31. 25- Grande, T., On the Thermodynamics of AgI Based Ionic Glasses and Melts Phys. Chem. Glasses. 1997, 38, 327–334. 26- Borjesson, L.; Martin, S. W.; Torell, L.; Angell, C. A. Brillouin Scattering in AgI Rich Glasses. Solid State Ionics, 1986, 18–19, 431–436.


Page 27 of 29


27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

27- Kobayashi, H.; Takahashi, H.; Hiki, Y. Viscosity of Glasses Near and Below the Glass Transition Temperature. J. Appl. Phys. 2000, 88, 3776-3778. 28- Hanaya, H.; Echigo, K.; Ogumi, M. Anomalous AgI Composition Dependence of the Thermal and Dielectric Properties of AgI–Ag2O–P2O5 Glasses: Evidence for the Formation of Amorphous AgI Aggregate Regions as Dominating the Fast Ag+ Ion Conduction. J. Phys Condens. Matter 2005, 17, 281-2292. 29- Bradley, J. N.; Greene, P. Potassium Iodide + Silver Iodide Phase Diagram. High Ionic Conductivity of KAg4I5. Trans. Faraday Soc. 1966, 62, 2069-2075. 30- Palles, D., Konidakis I., Varsamis C. P. E., Kamitsos E. I. Vibrational spectroscopic and bond valence study of structure and bonding in Al2O3containing AgI-AgPO3 glasses. RSC Advances 2016, 6, 16697-16710. 31- Jenkins, H. D. B.; Thakur, K. P. Reappraisal of Thermochemical Radii for Complex Ions. J. Chem. Educ. 1979, 56, 576-578. 32- Souquet, J.-L. In Solid State Electrochemistry; Bruce P., Ed.; Cambridge University Press: United Kingdom, 1995. 33- Kubaschewski, O.; Alcock, C. B.; Spencer, P. J. In Materials Thermochemistry, Pergamon Press Ed.; Oxford, United Kingdom, 1993. 34- Pathmanathan, K.; Micak, R.; Johari, G. P., Electrical Conduction by Fast Ion Transport in Molten (AgI)X(AgPO3)1−X Glasses. Phys. Chem. Glasses 1989, 30, 180–185. 35- Clement, V.; Ravaine, D.; Deportes C. Measurement of Hall Mobilites in AgPO3AgI Glasses. Solid State Ionics 1988, 28–30, 1572–1578. 36- Maier, J. In Physical Chemistry of Ionic Materials. Ions and Electrons in Solids, John Wiley & Sons, Ltd: Chichester, United Kingdom, 2004. 37- Souquet, J.L.; Nascimento, M.L.F.; Rodrigues, A.C.M. Charge Carrier Concentration and Mobility in Alkali Silicates, J. Chem. Phys. 2010, 132, 034704 -034704-7



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38- J. Janz In Molten Salts Handbook, Academic Press Inc.; London, United Kingdom, 1967. 39- Fraser, D.G. In Thermodynamics in Geology; Proceedings of The NATO Advanced Study Institute Held In Oxford, England, September 17-27, 1976. Dordrecht Ed: New York, USA, 1977.


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29

-2

x AgI (1-x) AgPO3

27

26

log (σ)

-5 24 -6 23 +

-7

log [Ag ] 22 0.0

0.1

0.2

0.3

0.4

x

TOC graphic


0.5

+

+

25

log [Ag ], [Ag ] in atoms cm

-1

-4

-3

x = 0.0 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5

-3


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Dissociation Equilibrium and Charge Carrier Formation in AgIâAgPO3

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Dissociation Equilibrium and Charge Carrier Formation in AgIâAgPO3